Luca's average trip will be 58 miles per hour.
How to calculate the speed?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:
= Distance / Time
= 464 / 8
= 58 miles per hour.
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Which system of equations can be graphed to find the solution(s) to x² = 2x + 3?
[y=x²+2x+3
y=2x+3
0
O
O
[y=x²-3
y=2x+3
[y=x²-2x-3
ly=2x+3
[y=x²
y=2x+3
Step-by-step explanation:
please refer to the sketch
The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,
So, the equation is x² = 2x+3
We can write this as,
x²-2x-3 = 0
Now, factorize to find the solution of the equation,
x²-3x+x-3 = 0
x(x-3)+1(x-3) = 0
(x+1)(x-3) = 0
x = -1 and x = 3
So, the solution of the equation is -1 and 3
However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,
y = x² and y = 2x+3
Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.
That is the x-coordinates of the points of intersection are the solutions.
Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]
Therefore, the system of equation is y = x² and y = 2x+3
Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3
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Lance Greene receives $2.20 per piece he
completes plus a 10% bonus for each piece he
completes over 180 pieces. Last week he
completed 210 pieces. Find his gross pay.
The gross price for the 210 pieces that Lance completed last week is $468.6.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
Amount received by Lance Greene for one piece = $2.20.
Also, Lance gets 10% bonus per piece after 180 pieces.
Given that, last week Lance completed 210 pieces .
Price for 210 piece = 210 x 2.20 = 462
Also, bonus gets by Lance on 30 pieces = 30 x 2.2 x 10/100 = 6.6
Total price = 462 + 6.6 = 468.6
The required gross price is $468.6.
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If c = d, then a + c = d + a true or false
Answer:
True
Step-by-step explanation:
First, you need to subtract a then that would make a 0
Answer: true
Step-by-step explanation: c and d are the same, so a+c and a+d will be the same
A growing amusement park is able to
sell 7 times as many tickets each year
as it did the year before. If you list the
number of tickets sold over time, what
kind of sequence will you see?
If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.
What is a geometric sequence?
A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Here,
We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:
x, 7x, 49x, 343x, .....
Verification:
7/1 = 49/7 = 343/49 = 7
Hence, this is a geometric sequence.
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Pls help me out here
All of the equations that are true include the following:
B. 56 + 70 = 14(4 + 5).
C. 28 + 49 = 7(4 + 7).
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
How to determine the true equation?In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
32 + 96 = 8(4 + 14)
32 + 96 = 32 + 112 (False).
56 + 70 = 14(4 + 5).
56 + 70 = 56 + 70 (True).
28 + 49 = 7(4 + 7).
28 + 49 = 28 + 49 (True).
27 + 36 = 3(9 + 13)
27 + 36 = 27 + 39 (False).
25 + 35 = 5(5 + 6)
25 + 35 = 25 + 30 (False).
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what is the experimental probability of spinning a white or yellow?
PLEASE PLEASE PLEASE HURRY ITS DUE TOMORROW!!!!!!
yellow / 5
blue / 12
green / 8
white / 9
red / 6
The experimental probability of spinning a white or yellow is 7/20
How to determine the experimental probability of spinning a white or yellow?From the question, we have the following parameters that can be used in our computation:
Outcomes of experiments
The outcomes of experiments are given as
yellow / 5
blue / 12
green / 8
white / 9
red / 6
The experimental probability of spinning a white or yellow can be calculated using the following equation
P(White or Yellow) =P(White) + P(Yellow)
Substitute the known values in the above equation, so, we have the following representation
P(White or Yellow) = (9 + 5)/5 + 12 + 8 + 9 + 6)
Evaluate the sum
P(White or Yellow) = 14/40
Simplify
P(White or Yellow) = 7/20
Hence, the probability is 7/20
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Complete the square for the expression. Then factor the trinomial.
x2 - 6x
Expression:
Factored form:
Expression: x² - 6x + 9
Factored form: (x - 3)²
Using the concept of factorization.
What is factorization?The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.
Given that,
x² - 6x
Now, to find the value of c = (b/2)²
divide the coefficient of x by 2.
So, divide 6 by 2 we get: ( -1.3)²
Next, multiply -1 by 3: (-3)²
Now, raise -3 to the power of 2, we get: 9
So, the expression becomes: x² - 6x + 9
Factorized form: (x - 3) (x -3)
or we can write (x - 3)²
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Hannah simplified the radical below and wants someone to check the work (view image)
Answer:
4|x|y²√(3yz)
She forgot the absolute value sign on x, and she left out the exponent on y.
Step-by-step explanation:
Step 1 is correct.
x may be positive, zero, or negative.
√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.
√16 = 4
√3 = √3
√x² = |x|
√y² × √y² = √y^4 = y²
Since y² is always non-negative, there is no need for absolute value sign.
√y^4 = y²
Answer should be
4|x|y²√(3yz)
9. Marcus vegetable is drawing a plan for his garden. He graphs one corner at (-7.2, 2). He reflects (-7.2, 2) across the x-axis. Then Marcus reflects the new points across the y-axis. What shape is the vegetable garden?
Answer: To reflect a point across the x-axis, you need to change the sign of the y-coordinate. Therefore, the point (-7.2, 2) reflected across the x-axis becomes (-7.2, -2).
To reflect a point across the y-axis, you need to change the sign of the x-coordinate. Therefore, the point (-7.2, -2) reflected across the y-axis becomes (7.2, -2).
The resulting shape is a rectangle with one corner at (-7.2, 2) and the opposite corner at (7.2, -2).
Step-by-step explanation:
What is the growth rate in inches per hour of flowers that grew 5 inches in 10 hours ??
Answer:
1/2 or 0.5 inches per hour
Step-by-step explanation:
5 divided by 10 will get you this answer
Someone pls help!!
Construct a circle through points
X, Y, and Z.
Answer:
Here is an example. Check out the uploaded image.
Step-by-step explanation:
Draw Points XY using a Straight Line
Draw a bisector in the middle of the line
Repeat Procedure for lines XZ and YZ
Where the two lines meet is the Center
Extend the compass from the center to any point and complete the circle.
Goran wants to build a square frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.
What is a square?The wood left over after making the frame and the sandbox is 10 inches.A square is a two-dimensional figure that has four sides and all four sides are equal.Definition. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.A square is a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.Square is slang for a person who is conventional and old-fashioned, similar to a Fuddy-duddy. This sense of the word "square" originated with the American jazz community in the 1940s, in reference to people out of touch with musical trends.The area of a square is given as side².
We have,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
Thus,
The remaining wood is 10 inches.
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Five more than a number is greater than 26
State how many negative real roots there may be for the function.
f(x) = x³ +7x² - 5x + 19
4 or 2 or o negative real roots
2 or o negative real roots
3 or 1 negative real roots
1 negative real root
There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.
To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.
x³ +7x² - 5x + 19
the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.
There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"
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the ratio of students to adults at the open house is 9:7 suppose there are 832 students and adults at the open house. how many students are there
Answer:
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
students/adults = 9/7
You can then cross-multiply to find the value of "students":
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
Copy code
students/adults = 9/7
You can then cross-multiply to find the value of "students":
Copy code
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
Since the number of students must be an integer, the number of students at the open house is approximately 118 students.
Step-by-step explanation:
Your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost. How much did the shoes cost? Write and solve an equation, let s represent the cost of the shoes.
The equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost.
Let s represent the cost of the shoes.
Now, equation is
8% of s=10
8/100 ×s=10
0.08s=10
s=10/0.08
s=$125
Therefore, the equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
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Based on the experiment if a card is chosen 200 times how many times would you expect to pick a card without stripes?
The number of expected times to pick a card without strips is 130.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The percentage of stripes from the 120 times.
= 42/120 x 100
= 35%
Now,
Based on this experiment,
The number of strip cards out of 200 times.
= 35% of 200
= 35/100 x 200
= 35 x 2
= 70
The number of times to pick a card without strips.
= 200 - 70
= 130
Thus,
The expected number of times to pick a card without stripes is 130.
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The complete question is given below.
Use the rule x+8 to write a sequence of numbers. Then write the sequence as a list of ordered pairs. Start with and substitute at least six values for .
Answer:
Here is a sequence of numbers using the rule "x+8":
x+8=9 (x=1)
x+8=10 (x=2)
x+8=11 (x=3)
x+8=12 (x=4)
x+8=13 (x=5)
x+8=14 (x=6)
Here is the sequence of ordered pairs:
(1, 9)
(2, 10)
(3, 11)
(4, 12)
(5, 13)
(6, 14)
Please help me I can’t figure it out
The number of times each number divides is 8 divides LCM into 11 times
11 divides into LCM 8 times and 22 divides into LCM 4 times .
What is LCM ?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
The LCM of 8 , 11 and 22 is 88
∴ 8 divides into LCM 11 times
11 divides into LCM 8 times
22 divides into LCM 4 times
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A railroad crossing arm that is 20 feet long is stuck with an angle of elevation of 35". Find x and y in the illustration below.
Round to the nearest tenth as needed.
Note: The red line is NOT needed to solve this problem.
20 ft
35
yft
Select the correct response
Ox-32.9 feet; y=12.0 feet
x-11.5 feet, y-16.4 feet
x-12.0 feet, y-32.9 feet
x=16.4 feet, y=11.5 feet
< Previous
The angle of elevation of a 20-foot railroad crossing arm is fixed at 35 degrees. As necessary, round up to the next tenth. 20 ft, 35 ft, x -11.5 feet, y- 16.4 feet .
What is angle of elevation ?Between the horizontal line and the line of sight, an angle called the angle of elevation is created. The angle of elevation formula tan =QR/PR can be used to calculate the building's height (QR). Therefore, the building has 8 units of height. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, in the depression angle, the line of sight is downward and parallel to the ground.
When we multiply in algebra, we come before a variable with a number. In the same way, xy means to multiply variable x by variable y, while 7xy means to multiply variable x by variable y and then to multiply the entire expression by seven. Due to the complexity of how train-based questions are frequently presented, it is always advisable to read the question thoroughly before responding. After reading the question, try to use a formula in it; this may lead to a direct solution and save you time.
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a3 - c + b, when a=3, b=6, c=8
Answer:
7
Step-by-step explanation:
In order to find the answer to the equation, you must substitute the given values into the equation.
A^3 - C + B
We know that A = 3, B = 6, and C = 8
(3)^3 - (8) + (6)
9 - 8 + 6
1 + 6
7
Given equation (x+y)/3= 24 _ x
Rewrite the equation in slope intercept form .
Answer:
(y+72)
I'm not sure because your answer is not very clear
I’m confused HELP pls
On solving the equation n = za the value of a is obtained as a = n/z.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
To solve for a in the equation n = za, isolate a on one side of the equation.
Do this by dividing both sides by z:
n/z = (za) / z
On the right side, the z's cancel out, leaving -
n/z = a
So the solution is -
a = n/z
Therefore, the value of a that satisfies the equation n = za is equal to n divided by z.
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I REALLY NEED HELP!!!! ASAP!!! WORTH 50 POINTS!!!!!!
3. Kyle has a notebook for each of his 13 classes. He puts 5 stickers on
each notebook. There are 10 stickers on each sheet. How many
sheets of stickers will Kyle need? Write an equation to solve. Use a
variable for the unknown.
The number of sheets of stickers that Kyle needs will be 7 sheets.
How to explain the equation?The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, Kyle has a notebook for each of his 13 classes. He puts 5 stickers on
each notebook and there are 10 stickers on each sheet.
The number of sheets of stickers that Kyle needs will be:
= (13 × 5) / 10
= 65 / 10.
= 6.5
= 7 approximately
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Guys, how much triangles this picture has?
Answer:
6 for the number of triangles or 7 because all the triangles form a hole triangle
Step-by-step explanation:
Answer: The answer is 6. If you add the triangle that all the small triangles are within, then you would get 7.
list this from least to greatest -$25.18,$48.12,-$24.72,$47.72,-$24.12,$25.12
The listing of the given values from the least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.
What is a number line?A number line is defined as the expression that represents the location of real numbers as being a positive number or a negative number.
The negative values which are the least in the number line are usually higher in value than the greater numbers, while the greater values are higher for positive numbers.
Therefore,the arrangement of the given values from least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.
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You are a researcher studying the health habits of people living in a large rural area. In particular, you are interested in the amount of weight gained early in life.
You want to estimate the population mean of all weight gains for the area's baby girls in their first year. To estimate the population mean of all such weight
gains, you select a random sample of 15 baby girls from this area and you record the weight (in kg) each gained in their first year. Assume the population is
approximately normally distributed.
Based on your sample, follow the steps below to construct a 90% confidence interval of the weight gains in the first year for all the area's baby girls. (If
necessary, consult a list of formulas.)
(a) Click on "Take Sample" to see the results for your random sample.
Take Sample
Sample size:
0
Point estimate:
0
Number of baby girls
4
Sample standard deviation:
0
15
Sample mean
Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 90%
confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".
Standard error:
5.538
Margin of error:
Sample standard
deviation
1.921
X
Confidence
level
S
Critical value
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;
Standard deviation equals sd/√(n)
where, n = sample size and sd = standard deviation
Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)
where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].
being that,
sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )
sample mean, x =58.133
standard deviation, s =11.6
sample size, n =15
level of significance, alpha = 0.05
from standard normal table, two tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145
we use CI = x ± t a/2 * (sd/ √((n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]
= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]
= [ 51.708 , 64.558 ]
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
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The graph of a quadratic function with vertex (2, -4) is shown in the figure below.
Find the domain and the range.
101
پہلے
<+
-10
10
Write your answers as inequalities, using x or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
In the graph of a quadratic function with vertex (2, -4) is shown in the figure, the Domain: -∞ < x < ∞ and Range: -4 ≤ x < ∞.
What is quadratic function?When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic function.
A polynomial of degree 2 is referred to as such because the highest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. This function is algebraic.
Domain for this quadratic function is all possible values of x where function is defined.
Thus, Domain: -∞ < x < ∞
Range is the set of value functions that correspond to the value 'x.'
Range: -4 ≤ x < ∞
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Finding area of composite figure
Answer:
73
Step-by-step explanation:
so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:
A=l*w or A=b*h
which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this
A+C=
than thats your answer (it should be 12.)